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If a < b, is a < c?

(1) (a)(c) = 0
(2) a + b = 0

Statement 1 : a.c = 0, either a or c is 0. If c is 0 and a is 10, then a > c. again, if a = -2, c= 0, then a < c. so cannot determine whether a < c.

Statement 2: a + b = 0. Since a < b , so a must be a negative number. But we don't know if c is a 0, or positive or negative number. Not sufficient.

Together, a is negative and a*c = 0, so c is 0. Hence, a < c. Sufficient.

C is the correct answer.
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If a < b, is a < c?

(1) (a)(c) = 0
(2) a + b = 0

Let's evaluate each choice.
(i)Given a<b and ac=0. from this we can infer either a can be 0 or c can be 0. If one value is zero then other value can be anything so this one not sufficient.
(ii) a+b=0, a<b from here we can say a=-b; no info about c. So not sufficient.

Let's combine both and check:
ac=0, a+b=0, a<b from these we can say that a cannot be 0, should be -ve and c should be zero so we can conclude that a<c.
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